Calculus Examples

$x^{2} y^{2} + 5 x y - 24$

Step 1

Rewrite $x^{2} y^{2}$ as ${(x y)}^{2}$ .

${(x y)}^{2} + 5 (x y) - 24$

Step 2

Let $u = x y$ . Substitute $u$ for all occurrences of $x y$ .

$u^{2} + 5 u - 24$

Step 3

Factor $u^{2} + 5 u - 24$ using the AC method.

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Step 3.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 24$ and whose sum is $5$ .

$- 3, 8$

Step 3.2

Write the factored form using these integers.

$(u - 3) (u + 8)$

Step 4

Replace all occurrences of $u$ with $x y$ .

$(x y - 3) (x y + 8)$